The email, broadcast on BBC's Newsnight, states that Kelly spoke to "my colleague Susan Watts, science editor of Newsnight, who described him as a senior official intimately involved in pulling together the dossier".
During his own evidence to the committee, Gilligan had refused to name Kelly as his source and BBC chairman Gavyn Davies had insisted that the source should be protected.
But the email suggests Gilligan was prepared to identify the scientist as the source of his colleague's reports, if not his own.
Chidgey is bound to face criticism because he falsely suggested during the select committee's hearing that he had spoken to Watts.
Referring to Watts' quote of an anonymous source, Chidgey said to Kelly: "I understand from Miss Watts that this is her record of a meeting she had with you. Do you still agree with those comments?"
Kelly replied: "I do not recognise those comments."
Newsnight said Chidgey had admitted yesterday that he had not spoken to Watts. The journalist had told only her editor at the time of the identity of her source.
Giving evidence to the Hutton inquiry yesterday, Alastair Campbell, Downing St's director of communications, said he felt it was a "good thing" for Kelly's identity to be exposed in an effort to prove that Gilligan had embellished his report claiming that the Government had manipulated the Iraq dossier. Kelly was a "strong and resolute character", Campbell said.
Questioning Campbell, James Dingemans, QC, counsel for the inquiry, said: "A game of chicken was being played by two great big institutions with Dr Kelly in the middle."
Like Gilligan, Campbell was seeking to use Kelly's appearance before the select committee on July 15 to his advantage.
Three days later, the scientist was found dead in an Oxfordshire wood after apparently committing suicide.
The inquiry also heard evidence that Prime Minister Tony Blair acted as a moderating force, overruling an earlier call from Campbell and Defence Secretary Geoff Hoon for Kelly to appear before the committee.
Campbell denied responsibility for the leaking of Kelly's name to the media after the scientist had admitted discussing the dossier with Gilligan.
Campbell also said he did not insert into the dossier the claim that Saddam Hussein could launch weapons of mass destruction within 45 minutes.
Asked by Lord Hutton if he thought the source should be revealed, Campbell said: "I felt it was inevitable and ... possibly the only way we were going to be able to establish in the public and parliamentary mind that the Today allegations were false. From my perspective, it will have been a good thing but I emphasise that I did not do anything to bring it about."
Campbell had told the committee that the dossier's first draft, which he saw on September 10, included the 45-minute claim.
Yesterday, asked about a draft he saw on September 5 that lacked the claim, he said that was not a dossier at all. A fresh dossier was being drawn up by Joint Intelligence Committee chairman John Scarlett.
A BBC spokesman refused to confirm the contents of Gilligan's email. Campbell said in evidence that the email was "quite extraordinary".
Dingemans said it "rather looks like Mr Gilligan is using the foreign affairs select committee as a chance to get at the Government".
Former Scotland Secretary Helen Liddell said the revelation seemed to show Gilligan had tried to influence the line of questioning of the committee, before which he had appeared as a witness. But Michael Portillo, a former Defence Secretary, told BBC Radio 4 that MPs often received guidance for questions.
"If I had been on that committee I would have rung Gilligan up."
- INDEPENDENT
Hutton inquiry website
British Parliament Foreign Affairs Committee transcript:
Evidence of Dr David Kelly
Key players in the 'sexed-up dossier' affair
Herald Feature: Iraq
Iraq links and resources
